%0 Journal Article
%T Some results on characterization of finite group by non commuting graph
%J Transactions on Combinatorics
%I University of Isfahan
%Z 2251-8657
%A Darafsheh, Mohammad Reza
%A Yousefzadeh, Pedram
%D 2012
%\ 06/01/2012
%V 1
%N 2
%P 41-48
%! Some results on characterization of finite group by non commuting graph
%K non commuting graph
%K Nilpotent groups
%K Finite groups
%R 10.22108/toc.2012.1180
%X The non commuting graph $nabla(G)$ of a non-abelian finite group $G$ is defined as follows: its vertex set is $G- Z (G)$ and two distinct vertices $x$ and $y$ are joined by an edge if and only if the commutator of $x$ and $y$ is not the identity. In this paper we prove some new results about this graph. In particular we will give a new proof of Theorem 3.24 of [A. Abdollahi, S. Akbari, H. R, Maimani, Non-commuting graph of a group, J. Algebra, 298 (2006) 468-492.]. We also prove that if $G_1, G_2, ldots, G_n$ are finite groups such that $Z(G_i)=1$ for $i=1, 2,ldots, n$ and they are characterizable by non commuting graph, then $G_1 times G_2 times cdots times G_n$ is characterizable by non-commuting graph.
%U https://toc.ui.ac.ir/article_1180_0ca13861eb689e095c1f50d1542a1aa7.pdf